#include <math.h>  
#include <stdlib.h>  
#include <stdio.h>
#define N 1000  
/*定义复数类型*/
typedef struct {
	double real;
	double img;
}complex;


complex x[N], *W; /*输入序列,变换核*/
int size_x = 0;      /*输入序列的大小，在本程序中仅限2的次幂*/
double PI;         /*圆周率*/
void fft();     /*快速傅里叶变换*/
void initW();   /*初始化变换核*/
void change(); /*变址*/
void add(complex, complex, complex *); /*复数加法*/
void mul(complex, complex, complex *); /*复数乘法*/
void sub(complex, complex, complex *); /*复数减法*/
void output();/*输出快速傅里叶变换的结果*/




int main()
{
	int i;                             /*输出结果*/
	system("cls");
	PI = atan(1) * 4;
	printf("                                        输出DIT方法实现的FFT结果\n");
	printf("Please input the size of x:\n");//输入序列的大小  
	scanf("%d", &size_x);
	printf("Please input the data in x[N]:\n");//输入序列的实部和虚部  
	for (i = 0; i<size_x; i++)
	{
		printf("请输入第%d个序列：", i);
		scanf("%lf%lf", &x[i].real, &x[i].img);
	}
	printf("输出倒序后的序列\n");
	initW();//调用变换核  
	fft();//调用快速傅里叶变换  
	printf("输出FFT后的结果\n");
	output();//调用输出傅里叶变换结果函数  
	return 0;
}



/*快速傅里叶变换*/
void fft()
{
	int i = 0, j = 0, k = 0, l = 0;
	complex up, down, product;
	change();  //调用变址函数  
	for (i = 0; i< log(size_x) / log(2); i++)        /*一级蝶形运算 stage */
	{
		l = 1 << i;
		for (j = 0; j<size_x; j += 2 * l)     /*一组蝶形运算 group,每个group的蝶形因子乘数不同*/
		{
			for (k = 0; k<l; k++)        /*一个蝶形运算 每个group内的蝶形运算*/
			{
				mul(x[j + k + l], W[size_x*k / 2 / l], &product);
				add(x[j + k], product, &up);
				sub(x[j + k], product, &down);
				x[j + k] = up;
				x[j + k + l] = down;
			}
		}
	}
}



/*初始化变换核，定义一个变换核，相当于旋转因子WAP*/
void initW()
{
	int i;
	W = (complex *)malloc(sizeof(complex) * size_x);  //生成变换核  
	for (i = 0; i<size_x; i++)
	{
		W[i].real = cos(2 * PI / size_x*i);   //用欧拉公式计算旋转因子  
		W[i].img = -1 * sin(2 * PI / size_x*i);
	}
}



/*变址计算，将x(n)码位倒置*/
void change()
{
	complex temp;
	unsigned short i = 0, j = 0, k = 0;
	double t;
	for (i = 0; i<size_x; i++)
	{
		k = i; j = 0;
		t = (log(size_x) / log(2));
		while ((t--)>0)    //利用按位与以及循环实现码位颠倒  
		{
			j = j << 1;
			j |= (k & 1);
			k = k >> 1;
		}
		if (j>i)    //将x(n)的码位互换  
		{
			temp = x[i];
			x[i] = x[j];
			x[j] = temp;
		}
	}
	output();
}



/*输出傅里叶变换的结果*/
void output()
{
	int i;
	printf("The result are as follows：\n");
	for (i = 0; i<size_x; i++)
	{
		printf("%.4f", x[i].real);
		if (x[i].img >= 0.0001)printf("+%.4fj\n", x[i].img);
		else if (fabs(x[i].img)<0.0001)printf("\n");
		else printf("%.4fj\n", x[i].img);
	}
}


void add(complex a, complex b, complex *c)  //复数加法的定义  
{
	c->real = a.real + b.real;
	c->img = a.img + b.img;
}


void mul(complex a, complex b, complex *c)  //复数乘法的定义  
{
	c->real = a.real*b.real - a.img*b.img;
	c->img = a.real*b.img + a.img*b.real;
}


void sub(complex a, complex b, complex *c)  //复数减法的定义  
{
	c->real = a.real - b.real;
	c->img = a.img - b.img;
}

